Converging evidence that common timing processes underlie temporal-order and simultaneity judgments: a model-based analysis

Perception of simultaneity and temporal order is studied with simultaneity judgment (SJ) and temporal-order judgment (TOJ) tasks. In the former, observers report whether presentation of two stimuli was subjectively simultaneous; in the latter, they report which stimulus was subjectively presented first. SJ and TOJ tasks typically give discrepant results, which has prompted the view that performance is mediated by different processes in each task. We looked at these discrepancies from a model that yields psychometric functions whose parameters characterize the timing, decisional, and response processes involved in SJ and TOJ tasks. We analyzed 12 data sets from published studies in which both tasks had been used in within-subjects designs, all of which had reported differences in performance across tasks. Fitting the model jointly to data from both tasks, we tested the hypothesis that common timing processes sustain simultaneity and temporal order judgments, with differences in performance arising from task-dependent decisional and response processes. The results supported this hypothesis, also showing that model psychometric functions account for aspects of SJ and TOJ data that classical analyses overlook. Implications for research on perception of simultaneity and temporal order are discussed.

Fitting model-based psychometric functions to simultaneity and temporal-order judgment data: MATLAB and R routines

Research on temporal-order perception uses temporal-order judgment (TOJ) tasks or synchrony judgment (SJ) tasks in their binary SJ2 or ternary SJ3 variants. In all cases, two stimuli are presented with some temporal delay, and observers judge the order of presentation. Arbitrary psychometric functions are typically fitted to obtain performance measures such as sensitivity or the point of subjective simultaneity, but the parameters of these functions are uninterpretable. We describe routines in MATLAB and R that fit model-based functions whose parameters are interpretable in terms of the processes underlying temporal-order and simultaneity judgments and responses. These functions arise from an independent-channels model assuming arrival latencies with exponential distributions and a trichotomous decision space. Different routines fit data separately for SJ2, SJ3, and TOJ tasks, jointly for any two tasks, or also jointly for the three tasks (for common cases in which two or even the three tasks were used with the same stimuli and participants). Additional routines provide bootstrap p-values and confidence intervals for estimated parameters. A further routine is included that obtains performance measures from the fitted functions. An R package for Windows and source code of the MATLAB and R routines are available as Supplementary Files.

On the discrepant results in synchrony judgment and temporal-order judgment tasks: a quantitative model.

Research on the perception of temporal order uses either temporal-order judgment (TOJ) tasks or synchrony judgment (SJ) tasks, in both of which two stimuli are presented with some temporal delay and observers must judge the order of presentation. Results generally differ across tasks, raising concerns about whether they measure the same processes. We present a model including sensory and decisional parameters that places these tasks in a common framework that allows studying their implications on observed performance. TOJ tasks imply specific decisional components that explain the discrepancy of results obtained with TOJ and SJ tasks. The model is also tested against published data on audiovisual temporal-order judgments, and the fit is satisfactory, although model parameters are more accurately estimated with SJ tasks. Measures of latent point of subjective simultaneity and latent sensitivity are defined that are invariant across tasks by isolating the sensory parameters governing observed performance, whereas decisional parameters vary across tasks and account for observed differences across them. Our analyses concur with other evidence advising against the use of TOJ tasks in research on perception of temporal order.

The left visual field attentional advantage: No evidence of different speeds of processing across visual hemifields.

Temporal-order judgment (TOJ) and simultaneity judgment (SJ) tasks are used to study differences in speed of processing across sensory modalities, stimulus types, or experimental conditions. Matthews and Welch (2015) reported that observed performance in SJ and TOJ tasks is superior when visual stimuli are presented in the left visual field (LVF) compared to the right visual field (RVF), revealing an LVF advantage presumably reflecting attentional influences. Because observed performance reflects the interplay of perceptual and decisional processes involved in carrying out the tasks, analyses that separate out these influences are needed to determine the origin of the LVF advantage. We re-analyzed the data of Matthews and Welch (2015) using a model of performance in SJ and TOJ tasks that separates out these influences. Parameter estimates capturing the operation of perceptual processes did not differ between hemifields by these analyses, whereas parameter estimates capturing the operation of decisional processes differed. In line with other evidence, perceptual processing also did not differ between SJ and TOJ tasks. Thus, the LVF advantage occurs with identical speeds of processing in both visual hemifields. If attention is responsible for the LVF advantage, it does not exert its influence via prior entry.

A model for the time-order error in contrast discrimination.

Trials in a temporal two-interval forced-choice discrimination experiment consist of two sequential intervals presenting stimuli that differ from one another as to magnitude along some continuum. The observer must report in which interval the stimulus had a larger magnitude. The standard difference model from signal detection theory analyses poses that order of presentation should not affect the results of the comparison, something known as the balance condition (J.-C. Falmagne, 1985, in Elements of Psychophysical Theory). But empirical data prove otherwise and consistently reveal what Fechner (1860/1966, in Elements of Psychophysics) called time-order errors, whereby the magnitude of the stimulus presented in one of the intervals is systematically underestimated relative to the other. Here we discuss sensory factors (temporary desensitization) and procedural glitches (short interstimulus or intertrial intervals and response bias) that might explain the time-order error, and we derive a formal model indicating how these factors make observed performance vary with presentation order despite a single underlying mechanism. Experimental results are also presented illustrating the conventional failure of the balance condition and testing the hypothesis that time-order errors result from contamination by the factors included in the model.

Standardized environmental management systems as an internal management tool

In a principal-agent model we analyze the firm’s decision to adopt an informal or a standardized Environmental Management System (EMS). Our results are consistent with empirical evidence in several respects. A standardized EMS increases the internal control at the cost of introducing some degree of rigidity that entails an endogenous setup cost. Standardized systems are more prone to be adopted by big and well established firms and under tougher environmental policies. Firms with standardized EMS tend to devote more effort to abatement although this effort results in lower pollution only if public incentives are strong enough, suggesting a complementarity relationship between standardized EMS and public policies. Emission charges have both a marginal effect on abatement and a qualitative effect on the adoption decision that may induce a conflict between private and public interests. As a result of the combination of these two effects it can be optimal for the government to distort the tax in a specific way in order to push the firm to choose the socially optimal EMS. The introduction of standardized systems can result in win-win situations where firms, society and the environment get better off.